1.6.16 Minkowski Sum

INPUT OUTPUT

Input Description:
Point sets or polygons A and B, with n and m vertices,
respectively.

Problem:
What is the convolution of A and B, ie.
the Minkowski sum A+B = \{x+y| x\in A, y \in B\}?

Excerpt from
The Algorithm Design Manual:
Minkowski sums are useful geometric operations that can be used to
fatten objects in appropriate ways.
For example, a popular approach to motion planning for polygonal robots
in a room with polygonal obstacles fattens each of the obstacles by taking the Minkowski sum of
them with the shape of the robot. This reduces the problem to moving a point from the start to the goal using a
standard shortest-path algorithm. Another application is in shape simplification
where we fatten the boundary of an object to create a channel and then define as the shape the minimum link path
lying within this channel. Similarly, convolving an irregular object with a small circle will help smooth out the
boundaries by eliminating minor nicks and cuts.